Decomposing the transfer entropy to assess higher order effects in Cardiovascular Interactions*

Transfer Entropy (TE) can exhibit bias-either in deficiency or excess-during both pairwise and conditioned calculations, owing to high-order dependencies among the dynamic processes under consideration and the remaining processes in the system used for conditioning. To handle high order effects, instead of conditioning TE on all the measured processes except the driver and target, as in its fully conditioned version, or not conditioning at all, as in the pairwise approach, one can search for both the multiplets of variables that maximize information flow and those that minimize it, thus obtaining a decomposition of TE into unique, redundant, and synergistic atoms. This approach quantifies the relative importance of high-order effects compared to pure two-body effects while highlighting the processes that contribute to building these high-order effects alongside the driver. We employ this approach to analyze cardiovascular and cardiorespiratory interactions related to baroreflex and respiratory sinus arrhythma mechanisms.